Check out this video https://www.youtube.com/watch?v=HoKDTa5jHvg of the math.
A lot of other sources skip over the math to give you the big picture.
After that you will find the video very helpful in understanding the math.
Holy shit, this is one of the most well-produced, succinct, educational YouTube videos I've ever seen. Instantly subscribed.
The meta tl;dr is that diffusion is generally used for modern AI-image generation (with a lot of developments in that space), but the code workflows/Colab Notebooks are a mess and filled with technical debt, so a Hugging Face high-level approach for the tool makes sense.